The commands described in this section are used to partition a molecular system into "blocks" and allow for the use of coefficients that scale the interaction energies (and forces) between these blocks. This has a number of applications, and specific commands to carry out free energy simulations with a component analysis scheme have been implemented. The lambda-dynamics, an alternative way of performing free energy calculations and screening binding molecules, has also been implemented. Subcommands related to BLOCK will be described here. To see how to output the results of a dynamics run, please see DYNAMICS documentation (keywords are IUNLDM, NSAVL, and LDTITLE). Please refer to PDETAIL.DOC for detailed description of the lambda dynamics and its implementation. BLOCK was recently modified so that it works with the IMAGE module of CHARMM. As some changes to the documentation were necessary anyways, it was decided to also improve the existing documentation. The Syntax and Function section below are relatively unchanged; the added documentation is in the Hints section (READ IT if you are using BLOCK for the first time!). Comments/suggestions to boresch@tammy.harvard.edu. * Menu: * Syntax:: Syntax of the block commands * Function:: Purpose of each of the commands * Hints:: Some further explanations/hints * Limitations:: Some warnings...

Syntax of BLOCK commands BLOCk [int] Subcommands: miscellaneous-command-spec ! see *note miscom:(miscom.doc). CALL int atom-selection LAMBda real COEFficient int int real - [BOND real] [ANGL real] [DIHEdral real] [ELEC real] [VDW real] NOFOrce FORCe FREE_energy_evaluation [OLDLambda real] [NEWLambda real] - FIRSt int [NUNIT int] [BEGIn int] [STOP int] [SKIP int] - [TEMPerature real] [CONTinuous int] [IHBF int] [INBF int] [IMGF int] INITialize CLEAr Energy_AVeraGe [OLDLambda real] [NEWLambda real] - FIRSt int [NUNIT int] [BEGIn int] [STOP int] [SKIP int] - [CONTinuous int] [IHBF int] [INBF int] [IMGF int] COMPonent_analysis DELL real NDEL int [TEMPerature real] - FIRSt int [NUNIT int] [BEGIn int] [STOP int] [SKIP int] [IHBF int] [INBF int] [IMGF] int AVERage {DISTance int int} {STRUcture} [PERT] [TEMPerature real] [OLDLambda real] [NEWLambda real] - FIRSt int [NUNIT int] [BEGIn int] [STOP int] [SKIP int] LDINitialize int real real real real [real] RMBOnd RMANgle LDMAtrix LDBI int LDBV int int int int real real int LDRStart LDWRite IUNL int NSAVL int RMLAmbda {internal_energy_spec} internal_energy_spec ::== BOND THETa|ANGLe PHI|DIHEd IMPHi|IMPR SAVE UNSAve QLDM QLMC [MCTEmperature real] [FREQ int] [MCSTep int] [MAX real] MCIN int {real .... real} MCDI real MCRS MCLEar LANG [TEMP real] RSTP int real END

1) BLOCk [int] enters the block facility. The optional integer is only read when the block structure is initialized (usually the first call to block of a run) to specify the number of blocks for space allocation. If not specified, the default of three is assumed. 2) END exits the block facility. The assignment of blocks, the coefficient weighting of the energy function, the force/noforce option, etc. remain in place. For the terms of the energy function that are supported, each call to ENERGY (either directly or through MINIMIZE, DYNAMICS, etc. commands) results in an energy and force weighted as specified. The matrix of interaction coefficients is printed upon exiting. 3) CALL removes the atoms specified by "atom-selection" from their current block and assigns them to the block number specified by the integer. Initially all atoms are assigned to block 1. If atoms are removed from any block other than block 1, a warning message is issued. If blocks are assigned such that some energy terms (theta, phi, or imphi) are interactions between more than two blocks, a warning is issued when the END command is encountered. (Take such warnings seriously; this is a severe error and indicates that something is wrong. However, the problem might be not the CALL statement (or the atom selection) itself; quite possibly your hybrid molecule was generated improperly) 4) LAMBda sets the value of lambda to "real". This command is only valid when there are three blocks active. Otherwise multiple COEF commands may be used to set the interaction coefficients manually. LAMBda x is equivalent to (let y=1.0-x) COEF 1 1 1.0 COEF 1 2 y COEF 1 3 x COEF 2 2 y COEF 2 3 0.0 COEF 3 3 x 5) COEF sets the interaction coefficient between two blocks (represented by the integers) to a value (the real number). When the block facility is invoked, all of the atoms are initially assigned to block 1 and all interaction coefficients are set to one. The required real value (first specified) scales all energy terms expect those specific terms which are named with alternative corresponding scale factors. 6) NOFOrce specifies that in subsequent energy calculations, the forces are not required. This is economical when using the post-processing commands (FREE,EAVG,COMP). Forces may be turned back on with the FORCe command; this is necessary before running minimizations and dynamics if there was a prior NOFO command. 7) FREE calculates a free energy change using simple exponential averaging, i.e. the "exponential formula". If the old and new lambdas (OLDL,NEWL) are specified (can only be done when three blocks are active), the perturbation energy is calculated for these values (i.e. FREE gives you the free energy difference between NEWLambda and OLDLambda via perturbation from the lambda value at which your trajectory was calculated. If not, the current coefficient matrix is used (FREE should be used with three blocks, and the use of OLDL and NEWL is recommended). FIRSt_unit, NUNIt, BEGIn, STOP, and SKIP specify the trajectory/ies that is/are to be read (for a further description see the TRAJ command elsewhere in the CHARMM documentation). TEMPerature defaults to 300 K and gives the temperature value to be used in k_B*T. CONTinuous specifies the interval for writing cumulative free energies. A negative value causes binned (rather than cumulative average) values to be written. Be careful to make sure that you use correct non-bonded lists (see the hints section!) 8) INITialize is called automatically when the BLOCK facility is first entered and may also be called manually at some other point. All atoms are assigned to block one and all interaction coefficients are set to their initial value. 9) CLEAr removes all traces of the use of the BLOCK facility. The next command should generally be END, and then CHARMM will operate as if BLOCK had not ever been called. 10) EAVG The average value of the potential energy during a simulation can be calculated with the EAVG (Energy_AVeraGe) command. The parsing is very much like the FREE command above. The most frequent use of this command is to calculate the average value of dV/dlambda during the course of a simulation for use in thermodynamic integration. CONTinuous specifies the interval for writing cumulative free energies. A negative value causes binned (rather than cumulative average) values to be written. Be careful to make sure that you use correct non-bonded lists (see the hints section!) The command accepts the OLDL / NEWL option, similarly to FREE, but for EAVG it is recommended to set up the interaction matrix (using COEF commands) yourself -- see the hints section. 11) [COMP] The COMP module is essentially a modified version of the EAVG module which aside from calculating <dU/dl> = <U_1 - U_0> at a given value of lambda l(i) will also give you expectation values of this quantity at l(i+-1), l(i+-2) etc. based on perturbation theory. COMP requires 4 blocks. Put the usual WT (reactant) in block 2 and MUT (product) in block 3. Put the portion of the environment whose contribution to the free energy change is desired into block 4 (this can be everything else, or just a subset) (Note that the same can be achieved easily with the EAVG command) You have to set up your own coefficient matrix. Much of the parsing is like the EAVG command. CONT is not supported. Two special subcommands (required) are DELL and NDEL. The normal output of COMP is <U_1 - U_0> evaluated at the lambda of the simulation. However, COMP also evaluates the same ensemble averages perturbed to lambda = lambda +/- {0,1,2,...NDEL}*DELL. This (sometimes) helps the quadrature in thermodynamic integration. Note that NDEL must be at least 1, and DELL should not be zero. (You have to specify these values; the default values will lead to an invalid input, i.e. you bomb...) Be careful to make sure that you use correct non-bonded lists (see the hints section!) A word of warning: If your initial ensemble average (at the lambda of the simulation) is not well converged, then your perturbed values are most likely random numbers. The approach taken by COMP is theoretically sound, but it should only be applied if convergence has been established! The output format of COMP is somewhat messy: COMP first prints <dU/dl> = <U_1 - U_0> at lambda = lambda - NDEL*DELL lambda - (NDEL-1)*DELL ... lambda lambda + DELL ... lambda + NDEL*DELL; then it prints an average (integral) value over these results. The meaning of this last value is unclear to me. In earlier versions of this documentation, COMP has been recommended over EAVG. In my experience the opposite is true. There is little COMP can do which you can't do with EAVG (aside from obtaining expectation values for dU/dl). (Maybe the unclear output of the COMP module is the main reason why I don't like it). 12) [AVER] The AVERage command is used to extract ensemble average structural properties from a dynamics simulation. Features in this implementation allow averages taken over ensembles that are perturbed from that which the simulation corresponds to. This is particularly useful for calculating the average structure expected at lambda=0.0 from a simulation run at lambda=0.1, for example. One may calculate average structures [STRUcture] and average distances [DISTance int int; where the two integers are the atom numbers between which the average distance is requested], currently. The PERT keyword indicates that a perturbed ensemble from the dynamics trajectory is desired, with TEMPerature giving the temperature to use in the exponential for the perturbation (defaults to 300 K), OLDLambda and NEWLambda are the lambdas for which the simulation was run and for which the ensemble is requested, respectively (only valid if three blocks are active; if these are not specified, the perturbation energy is calculated with the current coefficient matrix), and the remaining keywords are used to specify the trajectory. NOTE: TO THE BEST OF MY KNOWLEDGE THIS COMMAND HAS NOT BE MAINTAINED (so you are on your own if you use it!) 13) LDINitialize specifies input parameters for running lambda dynamics. It sets up the value of lambda**2, the velocity of the lambda, its mass and reference free energy (or biasing potential). E.g, the following input lines set up parameters for the third lambda with [lambda(3)]**2 = 0.4, lambdaV(3) = 0.0, lambdaM(3) = 20.0, and lambdaF(3)=5.0 (note that lambdaF(1) should always be set to zero). LDIN 3 0.4 0.0 20.0 5.0 For more details, see Node Hints, section "lambda-dynamics simulations". 14) LDMAtrix will automatically map the input lambda**2 values onto the coefficient matrix of the interaction energies (and forces) between blocks. 15) LDBI provides an option on applying biasing potentials on lambda variables. The integer value specifies the total number of biasing potentials to be used. E.g, LDBI 3 will include total of 3 biasing potentials in the simulation. 16) LDBV sets up the specific form of the biasing potentials. At the moment, the functional form is of power law and allows three different classes (for details see "the actual simulations"). The input format is LDBV INDEX I J CLASS REF CFORCE NPOWER e.g. LDBV 2 2 3 3 0.0 50.0 4 will assign the second biasing potential acting between lambda(2) and lambda(3). The potential form belongs to the third class with reference value of zero, the force constant of 50 kcal/mol and the power of four. 17) LDRStart is used to restart the lambda dynamics runs. 18) LDWRite specifies the FORTRAN output unit No. and the frequency for writing lambda histogram by assigning an integer to IUNL and an integer to NSAVL. (IUNL and NSAVL can be reset in DYNAmic command, see *note dynamc:(dynamc.doc) ) 19) RMBOnd and RMANgle are used when no scaling of bond and angle energy terms is desired. 20) RMLA is used when no scaling of bond, angle, proper torsion, and improper torsion terms are desired. This option always works with block module. The keywords: "RMBOnd" and "RMANgle" work only in lambda-dynamics. COEF command can work in the same way when lambda-dynamics or hybrid-MC/MD are not used. e.g. "RMLA BOND" = "COEF real BOND 1.0" 21) SAVE saves the decomposed-energy file for post processing in the TSM module. This command gives a choice for free energy calculation with block module to get free energy without saving the trajectory file. The condition and the name for the decomposed-energy file can be defined in the dynamics module. (see dynamic.doc, keyword: IBLC, NBLC) 22) UNSAve removes the traces of the use of SAVE command shown above. 23) QLDM turns on lambda-dynamics option. LDIN command also turns on the lambda-dynamics option only when QLMC turns off. 24) QLMC turns on hybrid-MC/MD option. If QLMC option is on, LDIN commands do not activate the QLDM option. In this version, we do not re-assign the velocity of the atoms when chemical variables (lambda) are changed by MC method. Therefore, the kinetic terms suddenly change into the different phase space. The stochastic dynamics may diminish such artificial effects and help to reach the canonical ensemble. QLMC and QLDM are exclusive and latest choice is active. QLMC command should specify conditions for hybrid-MC/MD. e.g. QLMC MCTEmperature 300.0 FREQ 10 MCST 5 MAX 0.9 IN the above example, the temperature used for sampling the chemical space by MC method is 300.0 [Kelvin]; MC sampling works every 10 molecular dynamics steps (using for sampling of the atomic space); in one MC sampling, 5 trials are examined; the scale factor (lambda^2) for the selected ligand is assigned to 0.9 and the rest of ligands (L-1) have the scale factor 0.1/(L-1). Different temperature can be defined in the lambda-dynamics and hybrid MC-MD for atomic variables and chemical variables. 25) MCIN allows the intermediate states in which only two ligands have non-zero lambda values in hybrid-MC/MD method. e.g. (Three ligands system) MCIN 5 0.0 0.25 0.5 0.75 1.0 5 means that each ligand may have one these five scalings: 0.0, 0.25, 0.5, 0.75, and 1.0. In this condition, CHARMM recognizes the following chemical states: (SCALE FACTOR) STATE NO. LIG_A LIG_B LIG_C 1 1.0 0.0 0.0 2 0.0 1.0 0.0 3 0.0 0.0 1.0 4 0.25 0.75 0.0 5 0.75 0.25 0.0 6 0.25 0.0 0.75 7 0.75 0.0 0.25 8 0.0 0.25 0.75 9 0.0 0.75 0.25 10 0.5 0.5 0.0 11 0.5 0.0 0.5 12 0.0 0.5 0.5 26) MCDI (increment) specifies the step size to move in lambda chemical movement. It allows intermediate states in which more than two ligands can have non-zero lambda values in hybrid-MC/MD method. "MCDI" requires the uniform interval for the definitions of the intermediate states. Step size must satisfy: Stepsize = 1.0/integer. Example: Three ligands system MCDI 0.25 ! 0.25 shows the step size to move in lambda chemical movement. In this condition, CHARMM recognizes next chemical states. (SCLE FACTOR) STATE NO. LIG_A LIG_B LIG_C 1 1.0 0.0 0.0 2 0.0 1.0 0.0 3 0.0 0.0 1.0 4 0.25 0.75 0.0 5 0.75 0.25 0.0 6 0.25 0.0 0.75 7 0.75 0.0 0.25 8 0.0 0.25 0.75 9 0.0 0.75 0.25 10 0.5 0.5 0.0 11 0.5 0.0 0.5 12 0.0 0.5 0.5 13* 0.25 0.25 0.5 14* 0.25 0.5 0.25 15* 0.5 0.25 0.25 It is possible for MCDI to produce a state in which three ligands take non-zero lambda values as shown with the asterisk (states 13, 14 and 15). "MCDI" seems to be more general, but "MCIN" allows non-uniform intervals. Thus, small step sizes can be assigned near end points. 27) MCRS ignores the force for lambda coming from the restraining potential in lambda-dynamics. It also ignores the restraining potential energy when chemical space is sampled by MC method. CMC/MD (Chemical Monte Carlo & molecular dynamics) method can be carried out by combining this command with QLMC. 28) MCLEar removes the traces of the use of QLMC command shown above. BLOCK CLEAr command also removes the all traces of the use of QLMC. MCLEar removes the traces of QLMC, while BLOCK CLEar removes all traces of the BLOCK module. 29) LANG turns on the interaction between lambda variable and langevin heatbath. In general, weak interaction between lambda variables and atoms produced large deviations from the target temperature. Different temperatures for lambda and atoms make nonequilibrium states and gave incorrect free energies. Therefore, we recommend that LANG turn on in any lambda-dynamics simulations. LEAP FROG integration method is required when using the LANG option. 30) RSTP adds the restraining potential for the unbound states ligands in lambda-dynamics and hybrid-MC/MD method to keep the physical low energy states. The type of the restraining potential used with RSTP is; R = alpha *(1 - lambda^2)* ( V - F ) i i i i It disappears when this ligands is in bound state (lambda=1). e.g. REST 3 0.3 3 means the type of the restraining potential; 0.3 shows the alpha value. There are three types for the restraining potential. Type 1 Both environmental atoms and the ligands feel the restraining potential. Umbrella sampling technique is used to remove the bias effect coming from the restraining potential. Type 2 The fixed average structure of the environmental atoms are assigned into Block 2. The restraining potential was calculated Ri is defined as a function of the fixed environmental atoms and the ligands. When the system is flexible and the difference between the real coordinates of the environmental atoms and fixed average coordinates are considerably large, the convergence tends to slow. Type 3 When the environmental atoms form the specific structure and vibrated around the minimum, the fixed average structure of the environmental atoms are similar to those of the real time coordinates. Therefore, the force coming from the restraining potential can be approximated zero as an average. If such a condition is satisfied, the environmental atoms can be ignored the force coming from the restraining potential and the ligands only feel the restraining potential.This approximation may have a problem when we handle the unstructured system like gas or liquid. The utility program, post_ldm_mcmd.exe is prepared for calculating the free energy differenes both without or with the restraining potential in lambda-dynamics or hybrid-MC/MD method. This program is saved in "support/post_analysis".

A warning is in order: the BLOCK module is quite user-unfriendly, AND the user (=you) has to know what he/she is doing, otherwise you won't get anywhere! (Of course, this could be a blessing in disguise) There are two applications for BLOCK: (i) Mere use as an energy partitioning facility, which may, e.g., very helpful as an alternative to the INTEraction energy command and (ii) use in free energy simulations. The focus here is on free energy applications. The following paragraphs assume that you are familiar with the theory of free energy difference simulations (e.g. Brooks et al. Advances in Chem. Physics, Vol. LXXI, 1988, chapter V); the emphasis here is to show how a rough tool as BLOCK can be used to implement the theory in a program and (of course) how to use it. Using BLOCK in order to calculate a free energy difference consists out of two rather dissimilar parts (as far as practical problems are concerned): (i) Run your system at various values of lambda and save trajectories. (ii) Postprocess the trajectories with the FREE or the EAVG command (possibly COMP), use the quantities which these modules give you to calculate the free energy difference. (i) The actual simulations ========================== It's probably easiest to use a concrete example, and the free energy difference between ethane and methanol in aqueous solution is used for that purpose. BLOCK is a so-called dual topology method (D. Pearlman, JPC 1994, 98, 1487) i.e. one has to duplicate any atom that is different with respect to any of its parameters. In the ethane/methanol case this means that you have to run with a solute which looks something like H1 \ /H4 \ C1E ---- C2-H5 H2 = { } \H6 / C1M --- OG / \HG1 H3 (and there is water.) Conceptually, this system is divided into three regions: environment: water, H1, H2, H3 (the region where nothing changes) reactant: C1E, C2, H4, H5, H6 (ethane half) product: C1M, OG, HG1 (methanol half), where of course the role of reactant and product is interchangeable. The steps involved to start running dynamics are as follows: (1) set up the hybrid (generate psf). In principle straightforward, but there is a practical pitfall: The autogenerate angles and dihedrals option(s) may produce artificial dihedrals/angles between the two/three parts of the system, e.g. you don't want angles H1-C1E-OG etc. or dihedrals H3-C1M-C2-H4 etc. Also, make sure to specify nonbonded exclusions between the reactant and product part, otherwise you'll get endless distance warnings and may even bomb if two atom positions coincide. (2) Place the hybrid into water (stochastic or periodic boundary conditions -- yes, IMAGE is now supported) as usual (3) Partition the system, i.e. enter BLOCK The following script fragment will do the trick: block 3 call 2 sele <reactant> end call 3 sele <product> end end (reactant and product have to be defined according to your system). BLOCK 3 initializes the block module with 3 blocks, all atoms are in block 1. The two CALL commands bring the reactant and product part of the system into block 2 and 3 respectively. (4) Run the necessary MD simulations. Let's assume that you decide to use the following values of lambda, lambda = 0.1, 0.3, 0.5, 0.7, 0.9. You want to start your simulation at lambda = 0.1 and you have already partitioned your system as shown in (3). (This information is kept within the same script between calls to block, but it is not saved in restart files or the psf, i.e. you have to repeat this step (as well as step (3)) in every input file). Enter block again, e.g. block lamb 0.1 end From now on interactions between the 3 blocks will be scaled according to the following matrix (lambda = l = 0.1 ==> 1-l = 0.9): block | 1 2 3 ------|-------------------- 1 | 1.0 1-l l 2 | 1-l 1-l 0. 3 | l 0. l Please note that BLOCK will first calculate an interaction, then check to which block the two atoms belong and scale the energy (and forces) appropriately. Therefore, if the distance between 2 atoms is zero (e.g. in the ethane/methanol example I would define C1M and C1E on top of each other!) then you need non-bonded exclusions, otherwise you encounter a division by 0 error! The LAMB command is a shortcut for the following sequence of COEF commands, the following code fragment should be self-explanatory: block coef 1 1 1.0 coef 1 2 0.9 coef 1 3 0.1 coef 2 2 0.9 coef 2 3 0.0 coef 3 3 0.1 end BLOCK only accepts and uses symmetric matrices, i.e. it doesn't matter whether you specify COEF 1 2 or COEF 2 1. Whenever you now call the energy routines, the energies/forces returned from them will be scaled according to the matrix you have set up. Minimizers and Dynamics can be used as always. So you are ready to run dynamics, and for arguments sake say that you run at every value of lambda 10,000 steps equilibration and 20,000 steps production (i.e. you save coordinates to trajectories) You don't need to save every step, every 5th to 20th step is probably more than enough. (If you saved every step you'd obtain highly correlated data, i.e. you have larger trajectories, but you won't gain anything in terms of convergence.) (ii) Post-processing -- how to obtain a free energy difference ============================================================== At this point in our example, you would have five trajectories corresponding to lambda = 0.1, 0.3, ..., 0.9 The BLOCK module now has to be used to obtain the average quantities you need for either the exponential formula (FREE) or thermodynamic integration (EAVG,COMP) from the trajectories you generated in step (i) (1) At this point, some issues regarding the non-bonded list have to be considered. No special considerations were necessary while running dynamics (aside from having some non-bonded exclusions where necessary); you just set up list updates as usual. During post-processing there are two considerations: (a) efficiency -- you just want to calculate the necessary subset of interactions (otherwise your post-processing run will take about as much time as the simulation itself), and (b) proper list-updating. (a) Efficiency: In none of the post-processing routines do you need the interactions between particles that belong to the environment; therefore you should avoid calculating them. This can be done easily by specifying cons fix sele <environment> end Note that this is not necessary, but it will reduce the CPU time necessary from hours to minutes (and results are identical!) However, if you had atoms belonging to reactant or product or both FIXed during the simulations in step (i), you MUST NOT FIX them now; otherwise you'll omit contributions. (b) List updating: While the efficiency considerations in principle are optional, you have to follow one of the two strategies below otherwise you'll get erroneous results. If you used IMAGE, you have to use the second protocol! Originally, the BLOCK post-processing commands would not do any list updating. This meant that you had to have a nonbonded list which would include all possible interactions before starting post-processing -- don't forget that you post-process over, e.g., 20 ps and particles will move quite far. You can easily create such a nonbonded list by specifying a CUTNB value of, e.g. 99. or 999. Ang (surely, all possible interactions will be included). A CHARMM script looks approximately as follows: !set up system (psf, initial coordinates) block !partition system end cons fix sele <environment> end ==> energy cutnb 99. <all other options as during dynamics> !open trajectories block !postprocessing end In this case, do not use the inbf, ihbf and imgf options of the post-processing commands, they will default to 0, i.e. no update. This approach, however, CANNOT work with IMAGES! Proper use of IMAGEs requires that the minimum image convention is checked periodically, i.e. particles have to be repartitioned between primary and image region. As the BLOCK post-processing commands now understand INBF, IHBF and IMGF, this doesn't pose a problem. However, the automated update is not supported (if you specify a negative value, you'll get a mild warning and the system will default to +1), and I recommend that you use 1 for all frequencies (don't forget, the frames in your trajectory are several steps apart, i.e. in general an update may be necessary) The above scheme now looks like: !set up system (psf, initial coordinates) block !partition system end cons fix sele <environment> end ! set up images if needed ==> energy <all options, incl. CUTNB, as during dynamics> !open trajectories block eavg <other options> inbf 1 ihbf ? (imgf 1) end Unless you have explicit hbond terms, ihbf can of course be 0! (Please note that there may or may not be problems with CRYSTAL, see Limitations section) (2) The actual post-processing commands. In the following I'll explain how to set things up for FREE, EAVG and COMP (as well as why). To speed up things further, you'll also want to specify the NOFOrce option at some point. FREE: This module allows you to calculate the necessary ensemble average for the exponential formula. Using our example, you can for example estimate the free energy difference between l=0.1 (a value at which you ran a trajectory) and l=0.0, or, based on your l=0.1 trajectory the free energy difference between l=0.0 and 0.2 (double wide sampling), i.e. A(0.0)-A(0.1) = -k_B*T*ln <exp[-(U(l=0.0)-U(l=0.1))/kT]>_(l=0.1) or A(0.2)-A(0.0) = -k_B*T*ln <exp[-(U(l=0.2)-U(l=0.0))/kT]>_(l=0.1) You should set up your system with 3 blocks and the usual environment, reactant and product partitions. Before entering block to issue the free command, you have to open the trajectory/ies. ! all the stuff shown above for non-bond lists open file unit 10 read name dat01.trj block free oldl 0.1 newl 0.0 first 10 nunit 1 [temp 300. - inbf 1 imgf 1] end or, for double wide sampling, the free line would be replaced by free oldl 0.0 newl 0.2 first 10 nunit 1 [temp 300. - inbf 1 imgf 1] Here dat01.trj is the trajectory which contains your 20 ps of dynamics at lambda = 0.1. Based on the oldl/newl values (which correspond to A(newl) - A(oldl)), FREE generates the appropriate interaction matrix, which it prints; I recommend that you try to understand why it generates this matrix! FIRST is the unit number of the first trajectory file (10 in our example), NUNIT is the number of trajectories (1 in our example). These (and the other options regarding the trajectories work as in any other post-processing command in CHARMM, see e.g. the TRAJ command) The update frequencies are optional depending on how you decided to handle your non-bonded updates. temp defaults to T=300 K, cf. equations above. If you specify CONT +n, you'll get a cumulative average every n steps; in this case the last value equals the final result; if you specify CONT -n, you'll get the average over every n frames, plus of course the final result at the end. Note that trajectories are not rewound after use; i.e. before any subsequent FREE (or EAVG,COMP) command you have to rewind (or reopen) them! Once you have all the free energy pieces you need, you simply add them up to obtain the free energy difference (beware of sign errors depending on how you defined oldl/newl) EAVG: The main use of this module lies in obtaining the required ensemble averages for thermodynamic integration. The most significant difference to EAVG is that you have to specify your own interactions matrix. BLOCK uses linear coupling in lambda in the potential energy function, i.e. V(l) = V0 + (1-l)*V_reac + l*V_prod, where V0 contains all the intra-environment terms, V_reac are the intra-reactant and reactant-env. interactions, and V_prod are the intra-product and product-env. interactions, respectively. The quantity of interest in TI is dV/dl; for the above potential energy function we have dV/dl = V_prod - V_reac It's very easy to obtain this quantity from EAVG. Use 3 blocks, partition the system as before. ! all the stuff shown above for non-bond lists open file unit 10 read name dat01.trj block coef 1 1 0. coef 1 2 -1. coef 2 2 -1. coef 1 3 1. coef 2 3 0. coef 3 3 1. eavg first 10 nunit 1 [inbf 1 imgf 1 cont +-n] end You will calculate the average interaction energy over all the frames in the trajectory according to the following (symmetric) matrix 0.0 -1.0 -1.0 1.0 0.0 1.0; i.e. it's easy to see that the above script will give you <V_prod - V_reac>_(l=0.1). If you post-process the other trajectories (l=0.3, 0.5, ..,0.9) in an analogous fashion, you just have to approximate the TI integral by the trapezoidal formula (for basic Newton Cotes formulae (open and closed) see, e.g., Numerical Recipes), i.e. in this case you would have dA = 0.2 * (dV(0.1)+dV(0.3)+...+dV(0.9)), where dV(0.1) = <V_prod - V_reac>_(l=0.1), etc. The above is an example of the basic use of EAVG. You automatically get the formal components according to interaction type. Cont +-n works similarly to the FREE case. If you wanted to exclude the intramolecular contributions from ethane and methanol you could set up a slightly different coefficient matrix, i.e. coef 1 1 0. coef 1 2 -1. coef 2 2 0. coef 1 3 1. coef 2 3 0. coef 3 3 0. and you'll get only the solute-solvent contributions. You can use more blocks (m > 3) to extract only a subset of interactions, e.g. block 1: environment - x block 2: reactant block 3: product block 4: x, where x is the region of interest, e.g. a specific sidechain in a protein (but not the one that is mutated!) Using EAVG with an appropriate coefficient matrix, e.g. coef 1 1 0. coef 1 2 0. coef 1 3 0. coef 1 4 0. coef 2 2 0. coef 2 3 0. coef 2 4 -1. coef 3 3 0. coef 3 4 1. coef 4 4 0. will give you (after integration over lambda) the free energy contribution of the interaction of sidechain x with the mutation site. Note that such formal free energy components may be (strongly) path-dependent. These last two examples have hopefully provided a flavor of what can be done with the EAVG module. COMP: This module is also used for thermodynamic integration. It always operates with four (and only four) blocks, just as the advanced example last given for EAVG, so it facilitates COMPonent analysis. Here I want to focus on the second unique aspect of COMP, it's capability to extrapolate additional datapoints, and so I consider in the framework of our ethane/methanol example the "special" case where I want the total free energy difference (as before in EAVG). In order to do this, the system needs to be partitioned as follows block 1: -- block 2: reactant block 3: product block 4: environment Whereas EAVG gave us <V_prod - V_reac>_l only for those lambda values at which we had actually done the simulations, COMP gives us additional values via perturbation (see Bruce Tidor's thesis). Using ! all the stuff shown above for non-bond lists open file unit 10 read name dat01.trj block coef 1 1 0. coef 1 2 0. coef 1 3 0. coef 1 4 0. coef 2 2 -1. coef 2 3 0. coef 2 4 -1. coef 3 3 1. coef 3 4 1. coef 4 4 0. comp first 10 nunit 1 [inbf 1 imgf 1] dell 0.06667 ndel 1 end will now give us <V_prod - V_reac>_l at l=0.03334, l=0.1 and l=0.16667. If we use the same script on the other trajectories, we have 15 instead of 5 datapoints for the integration, i.e. we can obtain dA as dA = 0.06667 * (dV'(0.03334)+dV(0.1)+...+dV'(0.96667)), where dV(0.1) = <V_prod - V_reac>_(l=0.1), etc. and the ' indicates that this is a perturbed quantity. In principle, this should give a better numerical integration; however, in practice everything depends on how well your actual data (l=0.1, 0.3, ...,0.9) are converged. There is no check whether your ndel/dell combination is meaningful; and you cannot run COMP without using the perturbation feature, i.e. NDEL should be set to at least 1 (valid values are 1 through 5). The defaults (if you don't specify ndel/dell) lead to an invalid input (This should be fixed...) (iii) Lambda-dynamics simulations ================================= In an efforts to make the transition from using previous subcommands to running the lambda dynamics as smoothly as possible, we purposely parallel new syntax after the COEF subcommand. There are total of eight new keywords for setting up new dynamics. They are classified according to their functionality. (a) LDINitialize and LDMAtrix These two keywords are basic commands for starting the lambda dynamics run. The correct use of them is tied together with the BLOCK and CALL commands. Using the same example as the one given in "the actual simulations", the input script fragment will be as following: block 3 call 2 sele <reactant> end call 3 sele <product> end LDIN 1 1.0 0.0 20.0 0.0 LDIN 2 0.9 0.0 20.0 0.0 LDIN 3 0.1 0.0 20.0 0.0 LDMA end Here, the LDINitialize command models after the COEF command with the format LDIN INDEX LAMBDA**2 LAMBDAV LAMBDAM LAMBDAF Several comments are in order. First, notice that [lambda(1)**2] = 1.0 and [lambda(2)]**2 + [lambda(3)]**2 = 1.0. They are quite similar to the inputs of COEF subcommand. However, since one index instead of a pair is required here, only diagonal elements of the interaction coefficient matrix are specified. To fill up the matrix, LDMA is provided to finish the job automatically. In general, if there is total of N blocks, the first one is by default assumed to be the region where nothing changes. Therefore, [lambda(1)**2] = 1.0 is always true. The condition N ____ \ / [lambda(i)**2] = 1.0 (1) ---- i = 2 has to be satisfied for the partion of the system Hamiltonian. Due to some technical reasons in our implementation (details see PDETAIL.DOC), we have used [lambda(i)**2] instead of lambda(i) in our partion of the system Hamiltonian. Next, to make sure the above condition is met at any given simulation step, we have also enforced a condition containing velocities of the lambda variables N ____ \ / lambda(i)*lambdaV(i) = 0.0 (2) ---- i = 2 We used lambdaV(i) = 0.0 in the above script just to simplify the input. As far as the mass parameter lambdaM is concerned, the minimum requirement is that the value of mass has to be chosen such that the time step (or frequency) of lambda variables is consistent with that used for spatial coordinates x, y, z. Since the lambda variable is introduced into the system by using extended Lagrangian, considerations gone into the similar quantities, such as the adjustable parameter Q in a Nose thermostat are applicable to the choice of lambdaM. Some crude estimation can be made by examining the derivative of the system Hamiltonian with respect to the lambda, the curvature (simple harmonic approximation) or energy difference between two end-point states (0 and 1). Our experience has indicated that a conservative choice of the mass, i.e. a little bit heavier mass than that of the crude estimate, serves us well so far. The biasing potential LAMBDAF has two functions: (1) In the screening calculations LAMBDAF corresponds to the free energy difference of the ligands in the unbound state. Such calculations can identify ligands with favorable binding free energy and a ranking of the ligands can be obtained from the probability of each ligand in the lambda=1 state; (2) In precise free energy calculations, LAMBDAF corresponds to the best estimate of free energy from previous calculations. Therefore the estimate of free energy can be improved iteratively. (b) LDBI and LDBV In order to provide better control over simulation efficiency and sampling space, an option of applying biasing (or umbrella) potentials is furnished. LDBI specifies how many biasing potentials will be applied and LDBV supplies all the details. The general input format is LDBV INDEX I J CLASS REF CFORCE NPOWER Let us look at the following script block LDBI 3 LDBV 1 2 2 1 0.2 40.0 2 LDBV 2 3 3 2 0.6 50.0 2 LDBV 3 2 3 3 0.0 20.0 2 end It states that there is total of 3 biasing potentials. The first one (INDEX = 1) is acting on lambda(2) itself (I = J = 2), the second one on lambda(3) and the third one is coupling lambda(2) and lambda(3) together. At the moment, three different classes of functional forms are supported: CLASS 1: __ | CFORCE*(lambda - REF)**NPOWER if lambda < REF V =| | 0 otherwise |__ CLASS 2: __ | CFORCE*(lambda - REF)**NPOWER if lambda > REF V =| | 0 otherwise |__ CLASS 3: V = CFORCE*[lambda(I) - lambda(J)]**NPOWER (c) LDRStart LDRStart is used only if for some reason, e.g. execution of EXIT command, the logical variable QLDM for the lambda dynamics has been set to false. In this case, to restart the dynamics, LDRStart can be used to reset QLDM = .TRUE.. However, if LDIN is also being used in restarting the dynamics, it will automatically reset QLDM. Therefore, LDRS does not need to be called in this case. (d) LDERite LDWRite provides specifications for writing out lambda dynamics, i.e. the histogram of the lambda variables, the biasing potential etc. The integer variable IUNLdm is the FORTRAN unit on which the output data (unformatted) are to be saved. The value of the integer NSAVL sets step frequency for writing lambda histograms. IUNLdm is defaulted to -1 and NSAVL is defaulted to 0. Both IUNLdm and NSAVl can be reset in DYNAmics command (Please refer to *note dynamc:(dynamc.doc) for details). the following script will set IUNLdm with unit No. 8 and NSAVL equal to 10: LDWRite IUNL 8 NSAVL 10 (e) RMBOnd and RMANgle Since each energy term is scaled by lambda, RMBOnd and RMANgle can prevent bond breaking caused by such scaling during dynamic simulations. Alternatively one can fix bonds (and angles) using SHAKE. But is is not always possible. END

(1) Please be advised (again) that the AVERage command is unsupported, and I would not be surprised if it does not work (anymore). Unless someone who understands this module better than I do maintains it, I recommend that we remove it. (2) BLOCK now coexists with IMAGE "peacefully" and essentially transperantly to the user. It works correctly for the case of a periodic water-box (cf. the block3.inp testcase). I would, however, check carefully whether things really work before I would use it on something fancier like infinite alpha helices. Similarly, it is not clear to me whether things work with the CRYSTAL facility. If one modifies block3 as to use CRYSTAL instead of IMAGE things (seem to) work. On the other hand, I know that I didn't support XTLFRQ in the post-processing routines as I don't understand its meaning. I'll fix things if someone is willing to help me with the bits and pieces I don't understand. (3) Bond and bond angle terms (including Urey-Bradleys). Be advised that if you run a simulation at lambda = 0 or lambda = 1 you may effectively remove bond (and bond angle terms) as they get scaled by zero. In other words, you would have ghost particles that can move freely through your systems, and this leads to all sorts of nasty side-effects. Furthermore, this approach is not sound theoretically (S. Boresch & M. Karplus, unpublished). So in general, avoid running at lambda = 0 and 1. If you have your bonds constrained you're safe as the constraint will keep things together (that won't take care of angles however!) In order to avoid artifacts from noisy, diverging bond and bond angle contributions throw them out during post-processing, e.g. by using the SKIP BOND ANGL UREY command before starting block post-processing. If you want to see what can go wrong, look at the block2 test-case...

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